Abstract

This new book by Gaylord and Nishidate is the third
by Gaylord on Mathematica applications, and the
second on applications in the physical sciences. In
this one, the authors focus exclusively on the Cellular
Automata (CA) approach for modeling complex
physical phenomena. For those not immediately familiar
with the approach, CA's approximate the interaction
of agents (which could be anything, from
molecules to bacteria, ants, and cars) by assigning a
finite number of states to each agent, and specifying
rules which dictate the next state of the agent as a
function of its own state and the states of its immediate
nearest neighbors. Then, the time evolution of
the system is deterministic after specifying the initial
state of each agent. As such, the approach is
extremely general, and can in general approximate
any macroscopic behavior of a collection of agents
that is otherwise described by differential equations.
The advantage of the approach becomes apparent
when modeling phenomena that become laborious to
describe via the differential equation approach, especially
when very many agents are concerned, and the
interactions are not simple. The most famous example
of a CA is the celebrated "Game of Life", which
displays complex emerging behavior that would be
extremely hard to describe analytically, even though
this must of course be possible in principle. This
example fittingly constitutes the first application of
the book.